Can anyone out there help me ?Q1. The lengths of the diagonals of a rhombus are 16 cm and 12 cm respectively.Find the length of each of its sides.Q2. The sum of two opposite angles of a 11gm is 130 degrees. Find the measure of each of its angles. Let ABCD is a rhombus and AC and BD are the diagonals that intersect each other at O. AC = 16 cm ; BD = 12 cm

Since diagonals of a rhombus bisect each other at right angle, then

∠ AOD = 900  and OA = OC = 8 cm ; OB = OD = 6 cm

Now, in Δ AOD ,

= (8)2 + (6)

= 64 + 36

So, each side of the rhombus is of 10 cm.

(2) Let ABCD is a parallelogram.

∠ B + ∠ D = 130

∠B + ∠B = 1300  ( Opposite angles of parallelogram are equal)

⇒∠B = 650 = ∠D

Now, ∠B + ∠C = 1800  (Adjacent angles of parallelogram are supplementary

⇒  ∠C = 1150

Now, ∠A = ∠C = 1150  (Opposite angles of parallelogram are equal)

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ANS1. As the diagonals of a rhombus bisect each other at 90 degrees.

16/2 = 8 and 12/2 = 6   , 64+36=100

length of 1 side is 10cm.

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